How to assign colors to Point Density based on data values?
The following script will generate a vertex color layer and assign a color for each vertex coordinate. Since you have a data structure with a color assigned to each vertex, and the vertex's coordinate, you can it to assign colors to each vertex.

The code is not straightforward, since the vertex color layer does not assign a single color to each vertex, but rather a color for each mesh loop. A single vertex can be a part of several loops, and thus have several colors. In a cube, for instance, each of the 8 vertices has 3 vertex colors.

This is why the find_loops_by_vert_co function takes in an object and a vertex coordinate, and returns the list of all loop indices that include a vertex with the same coordinate.

When iterating over the vertex coordinates, this function is called and assigns the desired color to each of the relevant loops. I'm using a specific data structure to include coordinate and color data. You'll have to adapt this script to match your own data structure.

import bpy

def find_loops_by_vert_co( o, co ):
    verts = o.data.vertices
    loopsInCo = []
    for poly in o.data.polygons:
        for i in poly.loop_indices:
            vCo = verts[ o.data.loops[ i ].vertex_index ].co[:]
            compare = [ round( e1, 3 ) == round( e2, 3 ) for e1, e2 in zip( vCo, co ) ]
            count   = len( [ e for e in compare if e ] ) == 3
            if count: loopsInCo.append( i )

    return loopsInCo

o = bpy.context.object

# Create a new vertex color layer
o.data.vertex_colors.new('Heat')
heat = o.data.vertex_colors['Heat']

coos2colors = [
    { 'co' : (1.0, 0.9999999403953552, -1.0),                  'color' : ( 0.5, 0.25, 0.25 ) },
    { 'co' : (1.0, -1.0, -1.0),                                'color' : ( 0.1, 0.6,  0.3  ) }, 
    { 'co' : (-1.0000001192092896, -0.9999998211860657, -1.0), 'color' : ( 0.9, 0.1,  0.2  ) },
    { 'co' : (-0.9999996423721313, 1.0000003576278687, -1.0),  'color' : ( 0.5, 0.8,  0.0  ) },
    { 'co' : (1.0000004768371582, 0.999999463558197, 1.0),     'color' : ( 0.4, 0.4,  0.9  ) },
    { 'co' : (0.9999993443489075, -1.0000005960464478, 1.0),   'color' : ( 0.1, 0.1,  0.6  ) },
    { 'co' : (-1.0000003576278687, -0.9999996423721313, 1.0),  'color' : ( 0.5, 0.5,  0.0  ) },
    { 'co' : (-0.9999999403953552, 1.0, 1.0),                  'color' : ( 0.5, 0.25, 0.25 ) }
]

for d in coos2colors:
    co, color = d['co'], d['color']

    vIndices = find_loops_by_vert_co( o, co )
    for vi in vIndices:
        heat.data[ vi ].color = color


You can use the vertex color layer in Cycles by using the Input --> Attribute node and plugging it into an Emission shader's color input.